Admission to a certain university is determined by an entry exam. The scores of this test are normally distributed with a mean of 450 and a standard deviation. Students who score in the top 35% will be offered admission. Elaine scores 487 on the test. Will she be admitted?

A. Yes, the probability of scoring a 487 on the exam is 0.778, so she will be admitted.
B. No, the top 35% is defined with a cut score of 492, so she will not be admitted.
C. No, the top 35% of all students have scores greater than or equal to 500, so she will not be admitted.
D. Yes, the top 35% is defined with a cut score of 480.25, so she will be admitted.

To determine if Elaine will be admitted to the university, we need to calculate the z-score for her score of 487. The z-score formula is given by:

z = (x - μ) / σ

where x is the individual score, μ is the mean, and σ is the standard deviation.

Substituting the given values, we have:

z = (487 - 450) / 50 = 0.74

Now, we need to find the probability associated with this z-score. We can use a standard normal distribution table or a calculator to find this probability. The probability of scoring a 487 on the exam is approximately 0.778.

Since the admission criteria states that students who score in the top 35% will be offered admission, Elaine's score falls within this range. Therefore, she will be admitted to the university.

Learn more about determining admission based on exam scores here:

https://brainly.com/question/28538820

#SPJ14